Prediction of melt viscosity flow curves at various temperatures for some olefin polymers and copolymers

A knowledge of the variation of melt viscosity of thermoplastic polymers with both shear rate and temperature is of considerable importance to plastics engineers as well as to polymer rheologists. The actual measurement of melt viscosity at a large number of temperatures and shear rates is frequently a tedious and time-consuming task. A technique has been developed, based upon the applicability of shear rate-temperature superposition, for predicting the flow curves of a number of olefin polymers and copolymers at various temperatures from experimental data obtained at one temperature for the material in question. The experimental validity for superimposing log shear stress—log shear rate curves at different temperatures along the log shear rate axis has been established for both high and low density polyethylenes, polypropylene, polybutene-1, and poly (ethylene vinyl acetate) copolymers. The temperature dependence of the resultant shift factors has been determined for each system, and the method of utilizing this information to predict viscosities as a function of temperature and shear rate is discussed.     

FLOW BEHAVIOR OF A THERMOTROPIC LIQUID CRYSTAL AROMATIC COPOLYESTER

The rheology of a thermotropic aromatic copolyester, especially the steady shear viscosity, has been studied and found to be very different and more complex than that of analogous conventional isotropic polymers. The viscosity has a power-law dependence on shear rate over a wide range. The temperature dependence is very high below 300°C, and is comparable to that of isotropic polyesters above that temperature. The end correction measured by capillary viscometry is large, which is normally indicative of high melt elasticity, but nevertheless the extrudate swell is very small. The melt viscosity is shear and temperature history dependent. Unexplained effects that have been observed include dependence of viscosity upon apparatus gap dimensions and upon shear history.     

HDPE/LLDPE reactor blends with bimodal microstructures—Part II: rheological properties

Reactor blends of polyethylene/poly(ethylene-co-1-octene) resins with bimodal molecular weight and bimodal short chain branching distributions were synthesized in a two-step polymerization process. The compositions of these blends range from low molecular weight (LMW) homopolymer to high molecular weight (HMW) copolymer and vice versa HMW homopolymer to LMW copolymer. The shear flow characteristics of these polymers in the typical processing range mostly depend on the molecular weight and MWD of the polymer and are independent of the short chain branch content. From oscillatory shear measurements, it was observed that the viscosity of HMW polymers was reduced with the addition of LMW material. For the polymers produced with this two-step polymerization process, the LMW homopolymer and HMW copolymer blends and HMW homopolymer and LMW copolymer blends were melt miscible, despite the large viscosity differences of the pure components.     

PVC melt rheology III: The effect of order and molecular weight on the shear rate dependence

The effect of polymerization temperature on the melt flow behavior of PVC of varying molecular weights has been studied over a wide shear rate range. For the same molecular weight, higher melt viscosities are observed for polymers prepared at lower temperatures. The shear rate dependence of the viscosity vs molecular weight plot is shown to be nonlinear over the shear rates examined. The inability to achieve a limiting zero-shear viscosity is discussed.     

A relationship between steady-state shear melt viscosity and molecular weight distribution in polystyrene

A model that relates to the molecular weight distribution (MWD) of high-density polyethylene to the steady-state shear melt viscosity has been applied to polystyrene melts. Relations are developed for predicting the rheological flow curve from the molecular weight distribution. Relationships are also developed to predict the MWD from the flow curve, although practical limitations to this procedure are given. From a consideration of predictions of the model and experimental data, it is concluded that the transition for a given molecular species from Newtonian to non-Newtonian flow is sharp. Additionally, the calculated empirical parameter that partitions the MWD into molecules that act in a Newtonian fashion and those that do not is shown to be equivalent to the largest molecular weight homolog that can still undergo Newtonian flow at a given shear rate for monodisperse fractions. The temperature dependence of the relaxation times is found to be somewhat higher than that predicted by the Rouse theory. An activation energy of 30 kcal/mole for η0 was used to fit the experimental viscosity data adequately at 190° and 225°C. The terminal relaxation spectrum for a narrow-MWD polystyrene standard is calculated and found to agree well for long relaxation times with that reported in the literature.     

高效催化剂对聚丙烯树脂分子量、分子量分布及纺丝性能的影响

燕山石化公司化纤地毯厂在采用高效催化剂前、后生产的新、老3702聚丙烯树脂(熔体流动指数MFI均为12—15)纺丝时,纺丝温度和纤维性能发生了显著变化。研究结果表明,这种差别主要是由于它们的分子量分布不同所引起的。新3702由于分子量分布较窄,与老3702聚丙烯树脂相比,即使在相同的MFI条件下,粘均分子量和零切变粘度也是较低的,因而纺丝温度也低。在工业生产中表明,除测定MFI外还应测定聚丙烯熔体在230℃下的零切变速率粘度,这对指导生产,能提供可靠依据。采用高效催化剂生产MFI为7—11的新3602牌号聚丙烯在燕山石化公司化纤地毯厂试纺中,废丝率下降了7%以上,成丝质量得到了提高。     

高等级HDPE管材树脂毛细管流变性能研究

采用单管毛细管流变仪,在不同温度下对高等级高密度聚乙烯(HDPE)管材树脂的熔体流动行为进行了研究,考察了剪切应力(τ<,w>)、剪切速率(γ)、挤出胀大及温度之间的关系.结果表明,高等级HDPE管材树脂熔体的剪切流动基本上服从幂律定律;熔体的表观黏度(η<,a>)对温度的依赖性大致上符合Arrhenius方程;η<,a>随τ<,w>和γ的增加而非线性减小;挤出胀大比随温度的升高而下降,随γ的增加呈非线性增大.     

Flow curve–molecular weight distribution: Is the solution of the inverse problem possible?

Several different theoretical models have been developed relating the flow curve of a polymer melt to its molecular weight distribution (MWD). These models allow calculation of the flow curve if MWD is known beforehand. According to one model the non-Newtonian behavior of a polymer melt is considered as a consequence of the gradual transition of high molecular weight (MW) fractions to the rubbery (non-fluid) state. This model, which gives realistic predictions of the flow curve, can be transformed into the equation for MWD, which appears to be directly related to the flow curve. The derived equation seems to present the exact solution of this inverse problem. Nevertheless, calculation tests show the instability of such a solution. This means that any inevitable experimental error in the flow curve measurements can lead to an unexpected and arbitrary wide divergence of the calculated MWD from the true one. However, if definite preset forms of MWD are used, the MWD width can be determined from the flow curve. This has been confirmed by experiments on different polymers, such as low-density polyethylene (LDPE), polyisoprene (PI), butyl rubber (BR), and polystyrene (PS).     

Analytical melting model for extrusion: Stress of fully compacted solid polymers

Our laboratory recently published several analytical equations that can be used to predict the melting rate of fully compacted solid polymers sliding on a heated metal surface, modeling the melting mechanism inside an extruder. These equations were obtained by seeking asymptotic solutions to the differential equations describing the melting mechanism, temperature, and shear-dependent viscosity of polymer melts. Following the same asymptotic approach, we successfully developed accompanying analytical equations for predicting the stress required to slide fully compacted solid polymers on a heated metal surface. The accuracy of these analytical stress equations was found to be reasonable, although not fully satisfactory, by comparing their predictions to the experimentally measured values. The accuracy of the stress calculation is directly related to the accuracy of the viscosity values at high shear rates. The consideration of the temperature and shear dependencies of melt viscosity is most important for accurate prediction of the stress, just as it is for the melting rate. The stress not only depends on the melt rheological properties of the polymer but also on the thermodynamic properties.     

Structural and rheological investigation of low density polyethylenes

Some low density polyethylenes (LDPE) with different melt flow index (MFI) or produced by different producers have been examined in detail by solvent gradient fractionation, ¹³C NMR analysis, FTIR spectroscopy and melt rheological measurements. It was found that the distribution curves of the samples resemble Wesslau's logarithmic-normal model. From branching analyses it can be concluded that the branching content in the analyzed LDPEs is independent from the molecular weight. Relations between viscosity curve parameters and molecular structure have been investigated. It has been found that the dependence of the first normal stress difference on the shear stress is influenced by polydispersity as well as by the character of samples branching.     

Controlled Degradation of Polypropylene: A Comprehensive Experimental and Theoretical Investigation

Experimental and modeling studies of the free-radical-induced degradation of polypropylene (PP) in the melt phase have been carried out. Experiments have been performed in a single-screw plasticating extruder using a peroxide as the free-radical source. Concentration of the peroxide was in the range 0.01–0.6 wt%. Results in the form of melt flow index (MFI) values, viscosity curves, and molecular weight distribution (MWD) of the produced resins are presented here. Based on these results, a constitutive equation describing the shear viscosity of the melt as a function of shear rate, temperature, and molecular weight has been derived. The extensional viscosity of these resins has been determined as a function of strain rate using Cogswell's analysis of converging flows. A previously developed kinetic model (plug flow) has been used to simulate the changes of the average molecular weights of the MWD, and a sensitivity analysis of this model has been carried out.     

Flow properties of molten ethylene–vinyl acetate copolymer and melt fracture

In an investigation of the behavior and formation mechanism of melt fracture the flow properties of molten ethylene–vinyl acetate (EVA) copolymer in the region of high shear rate were measured with a capillary-type rheometer. EVA copolymer differs slightly in flow curve from low-density polyethylene (LDPE); it seems, however, that the difference is due to the difference in molecular weight distribution (MWD) rather than to the materials themselves. The fluidity of molten EVA copolymer having a narrow MWD is equivalent to that of LDPE having a broad MWD and, generally, EVA copolymer has a higher fluidity than LDPE. It is expected that the fluidity increases with incorporation of vinyl acetate at the same MWD and the same M?_w. The critical shear rate increases with melt index and temperature. It cannot be found that the materials themselves and the MWD directly influence the critical point of melt fracture formation when the melt index is taken as a parameter. The critical viscosity (η_c) at which melt fracture forms decreases in an almost straight line with an increase of melt index. It was found from the studies of end correction and behavior of melt fracture formation that melt fracture occurs at the inlet of the die, and it is supposed that the melt fracture formation is caused by the elastic turbulence in the flow pattern due to a failure of recoverable shear strain at the die inlet.     

Molecular weight–viscosity relationships for poly(1,4-butylene terephthalate)

The correlation between number-average molecular weight and intrinsic viscosity in 60:40 phenol-sym-tetrachloroethane at 30°C for poly(1,4-butylene terephthalate) was established from endgroup determinations as well as by gel permeation chromatography, eqs. (1) and (10a). The GPC data also yielded relationships between weight- and z-average molecular weight and intrinsic viscosity, eqs. (10b) and (10c). Melt viscosities, corrected for the thermal history of the melt, were measured at shear stresses in the range of 0.02–0.55 MPa. Linear PBT melts were found to become non-Newtonian at a shear stress of approximately 0.11 MPa, independent of molecular weight within the range studied. Correlations between melt viscosity at low shear stress versus intrinsic viscosity are presented, as well as the dependence of melt viscosity in the non-Newtonian region on shear stress and low-stress (Newtonian) melt viscosity.     

Studies on binary and ternary blends of polypropylene with SEBS,PS, and HDPE. I. Melt rheological behavior

Studies are reported on melt rheological behavior of some binary and ternary blends of polypropylene (PP) with one or two of the following polymers: styrene–b-ethylene butylene–b-styrene triblock copolymer (SEBS), polystyrene (PS), and high-density polyethylene (HDPE). Blend composition of the binary blends PP/X or ternary blends PP/X/Y were so chosen that the former represent addition of 10 wt % X to PP while the latter represent 10 wt % addition of X or Y to the PP/Y or PP/X blend of constant composition 90:10 by weight, X/Y being SEBS, PS, or HDPE. Measurements were made on a capillary rheometer using both temperature elevation and constant temperature methods to study the behaviors prior to flow and in the flow region. Flow behavior, measured at a constant temperature (200°C) and varying shear stress (from 1.0 to 5.0 × 10⁶ dyn/cm²) to evaluate melt viscosity and melt elasticity parameters, is discussed for its dependence on the nature of the blend. Extrudate distortion, studied as a function of shear stress to evaluate the critical shear stress for the onset of extrudate distortion, showed differences in the tendency for extrudate distortion or melt fracture of these different blends. Also discussed is the effect of melt viscosity and melt elasticity on extrudate distortion behavior at the critical condition, which showed a unique critical value of the ratio (melt elasticity parameter)^1/2 (melt viscosity) for all these blends. Blend morphologies before and after the flow through the capillary are investigated through scanning electron microscopy, and their correlations with rheological parameters of the melt are discussed.     

Nonisothermal elongational behavior of blends with liquid crystalline polymers

Measurements of melt strength and breaking stretching ratio of several blends of thermoplastic polymers with liquid crystalline polymers are presented. The melt strength behavior depends not only on the viscosity of the blends but also on the temperature dependence of the viscosity. In particular, even if the viscosities of the blends are, at the extrusion temperature, lower than that of the thermoplastic matrices, the melt strength can be larger than that of the pure thermoplastics if its viscosity-temperature curve exceeds that of the matrices far from the solidification temperature. This behavior allows one to spin or film blow these blends despite the low viscosity.     

Extrusion of broad‐molecular‐weight‐distribution polyethylenes

The extrusion (single‐screw) characteristics of four high‐molecular‐weight, broad‐molecular‐weight‐distribution (MWD) polyethylene resins are discussed with an emphasis on the output rate. Despite the high molecular weights of the subject polyethylenes, their broad MWD (M_w/M_n range: 10 to 50) does not limit the pressure and torque developed during extrusion. However, the specific output of the four polymers was quite varied. First, the dynamics of the solids conveying section were examined with the highest‐molecular‐weight polyethylene exhibiting lower solids‐conveying rate than the other three. Further, a simple and quick method to evaluate the relative solids‐conveying efficiencies for various polyethylenes is presented. Finally, the dependence of the specific output on the melt rheology of the polymers is also addressed; specifically, the shear‐thinning extent of the melt in the metering section was found to influence output rate. The unique and counterintuitive temperature‐dependence of the shear‐thinning character for one of the four polymers will also be addressed in relation to its extrusion characteristics. Polym. Eng. Sci. 44:2266–2273, 2004. © 2004 Society of Plastics Engineers.     

MELT RHEOLOGICAL PROPERTIES OF TALC-FILLED ISOTACTIC POLYPROPYLENE COMPOSITES

The melt rheological properties of talc-filled isotactic polypropylene have been studied at talc concentrations of 0–33.3 vol% and at 493 K. The composites followed a power law model in the shear stress–shear rate dependence and were shear thinning. The apparent melt viscosity increased whereas the melt elasticity parameter “first normal stress difference” decreased as the talc concentration increased. Surface modification of the talc by a coupling agent LICA 38 modified the rheological properties through bonding and/or a plasticizing/lubricating effect.     

A simple analytical model for estimation of melt film variables in thermoplastic vibration welding

The strength of vibration welds of thermoplastics is governed by the weld zone microstructure, which in turn, is closely tied to the welding process variables, such as the thickness of the weld melt film and the temperature profiles therein. The mathematical model described in this report is aimed at describing the role of the rheology of the melt—specifically the magnitude and shear rate dependence of the melt viscosity—in governing the melt film variables during the steady state penetration phase (Phase III) of vibration welding. The steady state momentum balance and heat transfer within the melt film are solved by using the power law model for viscosity. Closed‐form analytical expressions are obtained for estimating the melt film thickness, the shear rates, and the temperature field within the film. This model has been used to estimate weld zone variables for four different polymers displaying a wide range of viscosities and shear thinning behaviors. POLYM. ENG. SCI., 54:499–511, 2014. © 2013 Society of Plastics Engineers     

Rheological and chemorheological studies of cyclic aryl ether ketone and aryl ether thioether ketone oligomers containing the 1,2-dibenzoylbenzene moiety

The melt stability, shear rate, and temperature dependence of steady-state shear viscosity of molten cyclic aryl ether ketone and thioether ketone oligomers containing the 1,2-dibenzoylbenzene moiety have been investigated. The isothermal chemorheology of the ring-opening polymerization of cyclic oligomers 4 and 9 in the presence of a nucleophilic initiator was also conducted. The cyclic aryl ether ketone oligomers are thermally stable in the melt, and their melt viscosity is several orders of magnitude lower than their high molecular weight linear counterparts. At a given temperature, the steady-state shear viscosity of the molten cyclics initially undergoes shear thinning as the shear rate increases, and once the shear rate is above 10 s⁻¹, the molten cyclic oligomers behave like Newtonian fluids. For the amorphous cyclic oligomers studied, the steady-state shear viscosity at 100 s⁻¹ at a given temperature only depends on their glass transition temperature. The cyclic aryl thioether ketone oligomers are thermally unstable in the melt and undergo ring-opening polymerization in the absence of an initiator to form high molecular weight linear polymers with a concomitant rapid increase in viscosity. The rate of change in viscosity increases with temperature and is promoted by the addition of a catalytic amount of elemental sulfur or a disulfide such as 2,2-dithiobis(benzothiazole). It is hypothesized that the ring-opening polymerization is initiated by the in situ generated thiyl radical(s) and proceeds via a free radical route. © 1996 John Wiley & Sons, Inc.